Pavel Alekseevich Saponov
- Professor:Faculty of Mathematics
- Pavel Alekseevich Saponov has been at HSE University since 2011.
Education and Degrees
* Candidate of Sciences
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
* Doctor of Sciences
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Student Term / Thesis Papers
- Bachelor
D. Remizovskaya, Commutative Subalgebras in the Universal Enveloping Algebra U(gl(n)). Faculty of Mathematics, 2020
D. Tyunyaev, Stability of Motion of a Mechanical System with Negative Feedback. Faculty of Mathematics, 2018
N. Bakaikina, Construction of Nondiagonal Matrix Units in the A_n Series Hecke Algebra. Faculty of Mathematics, 2017
- Master
N. Bakaikina, Representation Theory of Extended Reflection Equation Algebra. Faculty of Mathematics, 2019
A. Slinkin, Algebraic Properties of Quantum Yangian. Faculty of Mathematics, 2017
Courses (2020/2021)
- Classical Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematical Foundations of Quantum Mechanics (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Mathematics. Licenciatus (Bachelor’s programme; Faculty of Mathematics; 4 year, 1 module)Rus
- Mechanics (Bachelor’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
- Research Seminar "Braid Groups, Quantum Groups and Applications" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- Past Courses
Courses (2019/2020)
- Classical Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Research Seminar "Braid Group, R-matrices, and Quantum Groups" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Rus
Courses (2018/2019)
- Classical Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematics. Licenciatus (Bachelor’s programme; Faculty of Mathematics; 3 year, 4 module)Rus
- Research Seminar "Mechanics" (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Rus
- Research Seminar "Selcted Topics from Braid Group Theory and Qauntum Groups: Genesis and Applications of R-Matrices" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2017/2018)
- Classical Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Differential Equations (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
- Mathematical Practical Training 2 (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Mechanics (Bachelor’s programme; Faculty of Mathematics; 2 year, 4 module)Rus
- Research Seminar "The R-matrix: its Origin and Applications in the Braid Group Theory and in Quantum Groups" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2016/2017)
- Classical Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Quantum Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Research Seminar "The R-matrix: its Origin and Applications in the Theory of the Braid Groups and in Quantum Groups Theory" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
Courses (2015/2016)
- Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
- Quantum Field Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Research Seminar "Selected Topics in QFT and String Theory" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus
- String Theory (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
Publications25
- Article Saponov P. A., Slinkin A., Gurevich D. Bethe subalgebras in Braided Yangians and Gaudin-type models // Communications in Mathematical Physics. 2020. Vol. 374. No. 2. P. 689-704. doi
- Article Saponov P. A., Gurevich D. Braided Yangians // Journal of Geometry and Physics. 2019. Vol. 138. P. 124-143. doi
- Article Gurevich D., Pavel Saponov, Talalaev D. KZ equations and Bethe subalgebras in generalized Yangians related to compatible R-matrices // Journal of Integrable Systems. 2019. Vol. 4. No. 1. P. xyz005. doi
- Article Talalaev D., Saponov P. A. KZ equations and Bethe subalgebras in generalized Yangians related to compatible R-matrices // Journal of Integrable Systems. 2019. Vol. 4. No. 1. P. 1-16. doi
- Article Gurevich D., Saponov P. A., Talalaev D. Drinfeld–Sokolov reduction in quantum algebras: canonical form of generating matrices // Letters in Mathematical Physics. 2018. Vol. 108. P. 2303-2314. doi
- Chapter Saponov P. A., Gurevich D. From Reflection Equation Algebra to Braided Yangians, in: Recent Developments in Integrable Systemsand Related Topics of Mathematical Physics Vol. 273. Springer, 2018. doi P. 107-129. doi
- Article Gurevich D., P.A. Saponov. Generalized Yangians and their Poisson counterparts // Theoretical and Mathematical Physics. 2017. Vol. 192. No. 3. P. 1243-1257. doi
- Article Pavel Saponov, Gurevich D. Derivatives in noncommutative calculus and deformation property of quantum algebras // Journal of Noncommutative Geometry. 2016. Vol. 10. No. 4. P. 1215-1241.
- Article Gurevich D., Saponov P. A. Quantum geometry and quantization on U(u(2)) background. Noncommutative Dirac monopole // Journal of Geometry and Physics. 2016. Vol. 106. P. 87-97. doi
- Article Gurevich D., Rubtsov V., Saponov P. A., Skoda Z. Generalizations of Poisson Structures Related to Rational Gaudin Model // Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics. 2015. Vol. 16. No. 7. P. 1689-1707.
- Article Pavel Saponov, Gurevich D. Noncommutative Geometry and dynamical models on U(u(2)) background // Journal of Generalized Lie Theory and Applications. 2015. Vol. 9. No. 1. P. 1000215.
- Preprint Pavel Saponov, Gurevich D. Quantum geometry and quantization on U(u(2)) background. Noncommutative Dirac monopole / Cornell University Library. Series math.QA 1512.03495 "Quantum Algebra". 2015. No. 1512.03495.
- Article Gurevich D., Saponov P. A. Braided algebras and their applications to Noncommutative Geometry // Advances in Applied Mathematics. 2013. Vol. 51. P. 228-253. doi
- Article Pyatov P. N., Gurevich D., Saponov P. A. Braided Weyl algebras and differential calculus on U(u(2)) // Journal of Geometry and Physics. 2012. Vol. 62. No. 5. P. 1175-1188. doi
- Article Gurevich D., Saponov P. A., Pyatov P. N. Braided differential operators on quantum algebra // Journal of Geometry and Physics. 2011. Vol. 61. P. 1485-1501.
- Article Gurevich D., Pyatov P. N., Saponov P. A. Bilinear identities on Schur symmetric functions // Journal of Nonlinear Mathematical Physics. 2010. Vol. 17. No. supp01. P. 31-48. doi
- Article Saponov P. A., Gurevich D. Generic super-orbits in gl(m|n)* and their braided counterparts // Journal of Geometry and Physics. 2010. Vol. 60. No. 10. P. 1411-1423.
- Article Saponov P. A., Gurevich D. Wave operators on quantum algebras via noncanonical quantization // Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications. 2010. No. 109. P. 19-38.
- Article Saponov P. A., Gurevich D. Braided affine geometry and q-analogs of wave operators // Journal of Physics A: Mathematical and Theoretical. 2009. No. 42
- Article Gurevich D., Pyatov P. N., Saponov P. A. Representation theory of (modified) Reflection Equation Algebra of GL(m|n) type // St Petersburg Mathematical Journal. 2009. Vol. 20. P. 213-253.
- Article Gurevich D., Pyatov P. N., Saponov P. A. Spectral parameterization for power sums of a quantum supermatrix // Theoretical and Mathematical Physics. 2009. Vol. 159. P. 587-597.
- Article Gurevich D., Pyatov P. N., Saponov P. A. Reflection equation algebra in braided geometry // Journal of Generalized Lie Theory and Applications. 2008. Vol. 2. No. 3. P. 162-174.
- Article Gurevich D., Saponov P. A. Geometry of non-commtative orbits related to Hecke symmetries // Contemporary Mathematics Series. 2007. No. 433. P. 209-250.
- Article Pyatov P. N., Gurevich D., Saponov P. A. Hecke symmetries and characteristic relations on reflection equation algebra // Letters in Mathematical Physics. 1997. Vol. 41. P. 255-264.
- Article Pyatov P. N., Saponov P. A. Characteristic relations for quantum matrices // Journal of Physics A: Mathematical and Theoretical. 1995. Vol. 28. P. 4415-4421.
